Publication: 1/ƒ^(α) noise in spectral fluctuations of quantum systems
Loading...
Official URL
Full text at PDC
Publication Date
2005-03-04
Authors
Faleiro, E.
Salasnich, L.
Vranicar, M.
Robnik, M.
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Exportar
Abstract
The power law 1/ƒ^(α) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1/ƒ^(α) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.
Description
©2005 The American Physical Society. This work is supported in part by Spanish Government Grant Nos. BFM2003-04147-C02 and FTN2003-08337-C04-04. This work is also supported by the Ministry of Education, Science and Sports of the Republic of Slovenia.
UCM subjects
Unesco subjects
Keywords
Citation
[1] B. B. Mandelbrot, Multifractals and 1/f Noise (Springer, New York, 1999).
[2] A. Relaño, J. M. G. Gómez, R. A. Molina, J. Retamosa, and E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002).
[3] M. Robnik, report, CAMTP, December 2003 (to be published).
[4] H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, England, 1999).
[5] M.V. Berry and M. Tabor, Proc. R. Soc. London A 356, 375 (1977).
[6] O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
[7] G. Casati, F. Valz-Gris, and I. Guarneri, Lett. Nuovo Cimento 28, 279 (1980).
[8] M. Robnik, J. Phys. A 16, 3971 (1983).
[9] G. Veble, U. Kuhl, M. Robnik, H.-J. Stöckmann, J. Liu, and M. Barth, Prog. Theor. Phys. Suppl. 139, 283 (2000).
[10] M. Robnik, J. Phys. A 17, 1049 (1984); T. Prosen and M. Robnik, J. Phys. A 27, 8059 (1994); M. Robnik and T. Prosen, J. Phys. A 30, 8787 (1997).
[11] T. Prosen and M. Robnik, J. Phys. A 26, 2371 (1993).
[12] R. Markarian, Nonlinearity 6, 819 (1993).
[13] M. L. Mehta, Random Matrices, (Academic, New York, 1991).
[14] T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981).
[15] I. C. Percival, J. Phys. B 6, L229 (1973).
[16] M.V. Berry, Philos. Trans. R. Soc. London A 287, 237 (1977); M.V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); M. Robnik, in Atomic Spectra and Collisions in External Fields, edited by K. T. Taylor et al. (Plenum, New York, 1988) p. 265; M. Robnik, Nonlinear Phenomena in Complex Systems (Minsk) 1, No. 1, 1 (1998); M. Robnik, J. Phys. Soc. Jpn., Suppl. C 72, 81 (2003).
[17] T. Prosen and M. Robnik, J. Phys. A 27, 8059 (1994); T. Prosen, J. Phys. A 31, 7023 (1998); T. Prosen and M. Robnik, J. Phys. A 32, 1863 (1999); J. Malovrh and T. Prosen, J. Phys. A 35, 2483 (2002).
[18] E. Faleiro, J. M. G. Gómez, R. A. Molina, L. Muñoz, A. Relaño, and J. Retamosa, Phys. Rev. Lett. 93, 244101 (2004).